A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree

DOI10.1007/S10955-005-8029-3zbMath1149.82008OpenAlexW2054963410MaRDI QIDQ2492867

Utkir A. Rozikov

Publication date: 14 June 2006

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-005-8029-3

Mathematics Subject Classification ID

Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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Cites Work

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• Countable state space Markov random fields and Markov chains on trees
• Gibbs states in lattice models with two-step interaction
• Description of periodic extreme Gibbs measures of some lattice models on the Cayley tree
• Partition structures of the group representation of the Cayley tree into cosets by finite-index normal subgroups and their applications to the description of periodic Gibbs distributions
• On the purity of the limiting Gibbs state for the Ising model on the Bethe lattice.
• On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras
• On \(q\)-component models on Cayley tree: contour method
• Periodic Gibbs measures for the Ising model with competing interactions
• On Pure Phases of the Ising Model on the Bethe Lattices
• Gibbs States on Countable Sets

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